SELEX is a technique to identify DNA or RNA sequences that bind to a protein target with high affinity. The method uses principles from evolution to accomplish this goal. You start out with a large pool of random DNA or RNA sequences. You then mix these sequences with your nucleic acid binding protein (NBP) in order to isolate the sequences that bind to the NBP the best. Next, you amplify the sequences isolated from the binding step then repeat the procedure by binding these sequences to your NBP again.
As you perform more and more cycles of selection, the DNA or RNA sequences that bind to the NBP get amplified while the sequences that do not bind the NBP do not get amplified. Soon, the pool of sequences consists of only the most "fit" sequences that bind to the NBP with the highest affinity.
Here's the citation for the original paper describing the SELEX method:
Turek and Gold, 1990. Systematic Evolution of Ligands by Exponential Enrichment: RNA Ligands to Bacteriophage T4 DNA Polymerase. Science, 249: 505. http://dx.doi.org/10.1126/science.2200121[/url .
Here's a link to a classic paper applying the SELEX method to find sequences that bind strongly to histone proteins. Figure 1 shows a nice graphical overview of the method:
http://groups.molbiosci.northwestern.edu/widomweb/pdfpapers/New%20DNA%20Sequence%20Rules%20for%20High.pdf